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Parsnips are famously tricky to germinate. Seed must be fresh, and I can vouch for that having sown 2 rows with last years left over seed and getting a grand total of 3 'snips. Brand new packet and now have a lovely thick row of seedlings. Some people pre-germinate them by placing the seeds on a damp piece of kitchen towel, putting it inside a tuperware box, closing the lid, and placing it in the airing cupboard. Check on it daily and keep the towel damp and eventually you will see little tails growing, the roots. You can then VERY CAREFULLY plant these little babies into a seed drill on your allotment, but you don't want to go breaking the tail. You could sow again now, but you won't get monster 'snips. Even so, you will be rewarded with decent sized roots during the winter so it has to be worth a go.